While I'll agree a good ground is most important, I disagree with the advice given above...... Make sure the ground you currently have is in fact making good, clean and tight contact with the engine block. That is your main ground period! you should run a grounding strap to the frame but not to ground the starter, you are correct the starter gets it's ground from the block.

If your current ground cable is in bad shape .... replace it.

Here is how I'd trouble shoot this

If it's a 4 studed solenoid make you you didn't switch the "I" wire and the "S" wires on the solenoid. "S" wire should be purple and the "I" wire should be white or off yellow

If it's a 3 studed solenoid.....

a. Use a screw driver and jump across the battery cable stud on the starter and the actual motor stud on the starter.

If the starter doesn't spin, your battery cable is bad or the battery is dead.

b. If the battery is charged...... make sure the neg cable is connected and you have a good ground, then run a jumper cable from the pos post on the battery and touch the other end to the battery cable stud on the starter.

c. if it doesn't spin hook the other jumper cable to the neg post on the battery and connect the other end to one of the starter bolts....... touch the pos jumper cable to the battery stud on the starter. If it doesn't spin, you have a bad starter.

If the starter spins in test a. above but doesn't engage with the key switch........
Run a temp jumper from the pos post on the battery to the small "S" stud on the starter...... if the starter spins the wire from your ing switch has a fault. If the starter doen't spin with the jumper..... you have a fault in the solenoid.